Ultraviolet Finite Research Articles

Introduction to Nonlocal Field Theory Including Gravity

We give minireview of nonlocal field theory (infinite derivative field theory). We start with the discussion of the main peculiarities of nonlocal field theory on the example of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d = 4$$\\end{document} scalar \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\phi }^{4}}$$\\end{document}-model. The nonlocal \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\phi }^{4}}$$\\end{document}-model is ultraviolet finite, unitary, and macrocausal. One of the problems of nonlocal field theory is that the formfactor is an arbitrary entire function that makes the predictions extremely weak. We propose some additional principle that allows to fix the formfactor. Also we review the main results obtained in nonlocal quantum gravity, namely the nonlocal generalization of Einstein gravity leads to the superrenormalizable theory.

Ultraviolet finite resummation of perturbative quantum gravity

Abstract If the metric is chosen to depend exponentially on the conformal factor, and if one works in a gauge where the conformal factor has the wrong sign propagator, perturbative quantum gravity corrections can be partially resummed into a series of terms each of which is ultraviolet finite. These new terms however are not perturbative in some small parameter, and are not individually BRST invariant, or background diffeomorphism invariant. With appropriate parametrisation, the finiteness property holds true also for a full phenomenologically relevant theory of quantum gravity coupled to (beyond the standard model) matter fields, provided massive tadpole corrections are set to zero by a trivial renormalisation.

Interpolating gauge-fixing for Yang–Mills–Chern–Simons theory in D=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=3$$\\end{document}

The Yang–Mills–Chern–Simons theory in three-dimensional Minkowski space-time is studied in a gauge-fixing scheme which interpolates between the covariant gauge and light-cone gauge, the interpolating gauge-fixing. The ultraviolet finiteness of the theory is proved via the Becchi–Rouet–Stora (BRS) algebraic renormalization procedure, which allows us to demonstrate the vanishing of all β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-functions and all anomalous dimensions to all orders in perturbation theory.

Counting linearly polarized gluons with lattice QCD

We outline an approach to calculate the transverse-momentum-dependent distribution of linearly polarized gluons inside an unpolarized hadron on the lattice with the help of large momentum effective theory. To achieve this purpose, we propose calculating a Euclidean version of the degree of polarization for a fast-moving hadron on the lattice, which is ultraviolet finite, and no soft function subtraction is needed. It indicates a practical way to explore the distribution of the linearly polarized gluons in a proton and the linearly polarized gluon effects in hadron collisions on the lattice. Published by the American Physical Society 2024

Perturbative analysis of the Wess-Zumino flow

We investigate an interacting supersymmetric gradient flow in the Wess-Zumino model. Thanks to the nonrenormalization theorem and an appropriate initial condition, we find that any correlator of flowed fields is ultraviolet finite. This is shown at all orders of the perturbation theory using the power counting theorem for one-particle irreducible supergraphs. Since the model does not have the gauge symmetry, the mechanism of realizing the ultraviolet finiteness is quite different from that of the Yang-Mills flow, and this could provide further understanding of the gradient flow approach.

Radiative correction to lepton proton scatterings in manifestly Lorentz-invariant chiral perturbation theory

Manifestly lorentz-invariant baryon chiral perturbation theory is used to calculate the radiative correction of low energy elastic lepton proton scatterings. Corrections of differential cross section and charge asymmetry are given at next-to-leading order with nonzero lepton mass, in which both are infrared and ultraviolet finite. The results are basically consistent with previous predictions based on hadron model, but somewhat different from calculations based on heavy baryon chiral perturbation theory, especially in charge asymmetry.

Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

We present and discuss well known conditions for ultraviolet finiteness and asymptotic safety. The requirements for complete absence of ultraviolet divergences in quantum field theories and existence of a non-trivial fixed point for renormalization group flow in the ultraviolet regime are compared based on the example of a six-derivative quantum gravitational theory in d=4 spacetime dimensions. In this model, it is possible for the first time to have fully UV-finite quantum theory without adding matter or special symmetry, but by inclusion of additional terms cubic in curvatures. We comment on similarities and some apparent differences between the two approaches, but we show that they are both compatible to each other. Finally, we motivate the claim that actually asymptotic safety needs UV-finite models for providing explicit form of the ultraviolet limit of Wilsonian effective actions describing special situations at fixed points.

One-loop contributions to the decay H → νl̅νlγ in the Standard Model revisited

Abstract One-loop contributions to the decay H → νl̅νlγ with l = e, μ, τ within the Standard Model framework are revisited in this paper. We derive two representations for the form factors in this calculation. As a result, the computations are not only checked numerically by verifying the ultraviolet finiteness of the results but also confirming the ward identity of the amplitude. We find that the results have good stability with varying ultraviolet cutoff parameters as well as satisfying the ward identity. In phenomenological results, we study the partial decay widths for the decay channels in the two cases of the detected photon and invisible photon. Differential decay widths are also generated as a function of the energy of the final photon.

Generalized quantum electrodynamics: One-loop correction

In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in [Formula: see text] dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including a higher derivative field. This derivation, so-called generalized quantum electrodynamics, is motivated by the stability and unitarity features. This theory provides a natural and self-consistent extension of the quantum electrodynamics by enlarging the space parameter of spinor-gauge interactions. In particular, Haag’s theorem undermines the perturbative characterization of the interaction picture due to its inconsistency on quantum field theory foundations. To circumvent this problem, we develop our perturbative approach in the Heisenberg picture and use it to investigate the behavior of the operator current at one-loop. We find the two- and three-point correlation functions are ultraviolet finite, electron self-energy and vertex corrections, respectively. On the other hand, we also explain how the vacuum polarization remains ultraviolet divergent only at [Formula: see text] order. Finally, we evaluate the anomalous magnetic moment, which allows us to specify a lower bound value for the Podolsky parameter.

Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in N=1 supersymmetric gauge theories regularized by higher derivatives

For a general renormalizable $\mathcal{N}=1$ supersymmetric gauge theory with a simple gauge group we verify the ultraviolet (UV) finiteness of the two-loop matter contribution to the triple gauge-ghost vertices. These vertices have one leg of the quantum gauge superfield and two legs corresponding to the Faddeev--Popov ghost and antighost. By an explicit calculation made with the help of the higher covariant derivative regularization we demonstrate that the sum of the corresponding two-loop supergraphs containing a matter loop is not UV divergent in the case of using a general $\ensuremath{\xi}$-gauge. In the considered approximation this result confirms the recently proved theorem that the triple gauge-ghost vertices are UV finite in all orders, which is an important ingredient of the all-loop perturbative derivation of the Novikov-Shifman-Vainshtein-Zakharov relation.

On the ultraviolet finiteness of parity-preserving [formula omitted] massive QED[formula omitted

The parity-preserving UA(1)×Ua(1) massive QED3 is ultraviolet finiteness – exhibits vanishing β-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern–Simons mass parameter, and all the anomalous dimensions of the fields – as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi–Rouet–Stora (BRS) algebraic renormalization method in the framework of Bogoliubov–Parasiuk–Hepp–Zimmermann (BPHZ) subtraction scheme.

B -meson Ioffe-time distribution amplitude at short distances

We propose the approach for a lattice investigation of light cone distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$ meson, using the formalism of parton pseudodistributions. A basic ingredient of the approach is the study of short-distance behavior of the $B$-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA in coordinate space. We construct a reduced ITDA for the $B$ meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice.

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a “quantum point” converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in Doplicher et al. (2020), of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which seems difficult to remove. We solve this problem here by another strategy: the fields at a point in the interaction Lagrangian are replaced by the fields at a quantum point, described by an optimally localized state on QST; the resulting Lagrangian density agrees with the previous one after spacetime integration, but gives rise to a different interaction hamiltonian. But now the methods of perturbative Algebraic Quantum Field Theory can be applied, and produce an ultraviolet finite perturbation expansion of the interacting observables. If the obtained theory is tested in an equilibrium state at finite temperature the adiabatic cutoff in time becomes immaterial, namely it has no effect on the correlation function at any order in perturbation theory. Moreover, the interacting vacuum state can be obtained in the vanishing temperature limit. It is nevertheless important to stress that the use of states which are optimally localized for a given observer brakes Lorentz invariance at the very beginning.

Vacuum energy of the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion

Abstract By employing the $1/N$ expansion, we compute the vacuum energy $E(\delta\epsilon)$ of the two-dimensional supersymmetric (SUSY) $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ with $\mathbb{Z}_N$ twisted boundary conditions to the second order in a SUSY-breaking parameter $\delta\epsilon$. This quantity was vigorously studied recently by Fujimori et al. using a semi-classical approximation based on the bion, motivated by a possible semi-classical picture on the infrared renormalon. In our calculation, we find that the parameter $\delta\epsilon$ receives renormalization and, after this renormalization, the vacuum energy becomes ultraviolet finite. To the next-to-leading order of the $1/N$ expansion, we find that the vacuum energy normalized by the radius of the $S^1$, $R$, $RE(\delta\epsilon)$ behaves as inverse powers of $\Lambda R$ for $\Lambda R$ small, where $\Lambda$ is the dynamical scale. Since $\Lambda$ is related to the renormalized ’t Hooft coupling $\lambda_R$ as $\Lambda\sim e^{-2\pi/\lambda_R}$, to the order of the $1/N$ expansion we work out, the vacuum energy is a purely non-perturbative quantity and has no well-defined weak coupling expansion in $\lambda_R$.

Full . Full O(α) electroweak radiative corrections to e^+ e^-→ZH with beam polarizations at the ILCO(α) electroweak radiative corrections to e^+ e^-→ZH with beam polarizations at the ILC

We present full electroweak radiative corrections to with the initial beam polarizations at the International Linear Collider (ILC). The calculation is checked numerically by using three consistency tests that are ultraviolet finiteness, infrared finiteness, and gauge parameter independence. In phenomenological results, we study the impact of the electroweak corrections to total cross section as well as its distributions. In addition, we discuss the possibility of searching for an additional Higgs in arbitrary beyond the Standard Model (BSM) through ZH production at the ILC.

Maximally supersymmetric amplitudes at infinite loop momentum

We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to demonstrate the absence of poles at infinity of all MHV amplitudes through three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads us to discover that this theory does support non-vanishing residues at infinity starting at two loops, and the degree of these poles grow arbitrarily with multiplicity. This causes a tension between simultaneously manifesting ultraviolet finiteness---which would be automatic in a representation obtained by color-kinematic duality---and gauge invariance---which would follow from unitarity-based methods.

One-loop structure of the photon propagator in the standard model extension

We study radiative corrections on the photon propagator from the electroweak sector of the minimal Lorentz- and $CPT$-violating Standard Model Extension. We derive the most general Lorentz-violating ghost sector from BRST symmetry and renormalization theory. We introduce a Lorentz-violating nonlinear gauge that simplifies both the Higgs and gauge-sector extensions, which can be helpful in radiative corrections. At one loop, these sectors contribute to the $CPT$-even part of the photon propagator, characterized by the Riemann-type tensor $(k_F)_{\alpha\beta\mu\nu}$. We give exact results for the contributions to the SO(1,3) irreducible parts of $(k_F)_{\alpha \beta \mu \nu}$, namely, the Weyl-type tensor $(\hat{k}_F)_{\alpha \beta \mu \nu}$, the Ricci-type tensor $(k_F)_{\alpha \beta}$, and the curvature-type scalar $k_F$. In the Yukawa sector, one-loop contributions are ultraviolet finite, but most of them are unobservable due to finite renormalization. The only observable effect is a contribution proportional to $(k_F)_{\alpha \beta}$ that emerges via a dimension-6 term that is observer and gauge invariant. In the Higgs and gauge sectors, all the irreducible parts of the corresponding Riemann-type tensors receive divergent contributions, so they are observable. The only finite contribution corresponds to the dimension-6 term. We think of these contributions as radiative corrections to the renormalized tensors and assume that both effects are of the same order of magnitude to find bounds from vacuum birefringence and compare with the literature. Bounds on $(k_F)_{\alpha \beta}$ contributions, innocuous to birefringence, are also derived using limits on the renormalized tensor from Laser-Interferometer-Gravitational-Wave-Observatory data. We compare these bounds with the literature. Beta functions associated with $(\hat{k}_F)_{\alpha \beta \mu \nu}$ and $(k_F)_{\alpha \beta}$ are derived.

Erratum to: Cutkosky rules for superstring field theory

Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.

Casimir Energies for Isorefractive or Diaphanous Balls

It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with ε μ = 1 , a so-called isorefractive or diaphanous ball. Here we re-examine that example and attempt to extend it to an electromagnetic δ -function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented.